Character Motion in BGE: Hold Two keys at the same time
Solution

All you literally need to do to fix this is Click this button. (on all of your Motion Actuators)



Reason

When the Ad button is not clicked, each Actuator is setting the location, and is is overriding any other Actuators activated previously, regardless of whether or not they are still running. Enabling the Ad button makes each Actuator add to the change in location, enabling multiple Actuators to be executing at the same time.